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MULTIFRACTAL PROPERTIES OF THE SETS OF ZEROES OF BROWNIAN PATHS
independent random variables Brownian motion local time Hausdor
2015/9/29
In this paper we study Brownian zeroes in the neighborhood of which one can observe non-typical growth
rate of Brownian excursions. We interprete the multifractal curve for the Brownian zeroes calcul...
Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
multifractal dimensions Perturbation random matrix ensembles
2011/7/6
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain e...
Linearization effect in multifractal analysis: Insights from Random Energy Model analysis
Multifractal analysis linearization effect compound Poisson motion
2011/3/3
The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of di...
Linearization effect in multifractal analysis: Insights from Random Energy Model analysis
Linearization effect multifractal analysis Random Energy Model analysis
2011/1/4
The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of di...
Multifractal structure of Bernoulli convolutions
Multifractal structure Bernoulli convolutions
2010/11/15
Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. T...
Optimal transport for multifractal random measures. Applications
Random measures multifractal processes optimal transport metric KPZ
2010/11/26
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new not...
Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism
Borel measures Hausdorff dimension Multifractal anal-ysis Baire categories
2010/11/29
In this article, we prove that in the Baire category sense, measures supported by the unit cube of Rd typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifracta...